MCQ
If the equation $4x^2- 3kx + 1 = 0$ has equal roots then $k = ?$
- A$\pm\frac{2}{3}$
- B$\pm\frac{1}{3}$
- C$\pm\frac{3}{4}$
- ✓$\pm\frac{4}{3}$
✓
Answer
Correct option: D.
$\pm\frac{4}{3}$
Since the roots of the equation $4 {x}^2-3 {kx}+1=0$ are equal,
$D = 0$
$\Rightarrow b^2-4 a c=0$
$\Rightarrow(-3 k)^2-4 \times 4 \times 1=0$
$\Rightarrow 9 k^2-16=0$
$\Rightarrow 9 k^2=16$
$\Rightarrow\text{k}^2=\frac{16}{9}$
$\Rightarrow\text{k}=\pm\frac{4}{3}$
$D = 0$
$\Rightarrow b^2-4 a c=0$
$\Rightarrow(-3 k)^2-4 \times 4 \times 1=0$
$\Rightarrow 9 k^2-16=0$
$\Rightarrow 9 k^2=16$
$\Rightarrow\text{k}^2=\frac{16}{9}$
$\Rightarrow\text{k}=\pm\frac{4}{3}$
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